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JEE Previous Year Question

$The number of common tangents to the circles x^{2} + y^{2} - 4 x - 6 y - 12 = 0 and x^{2} + y^{2} + 6 x + 18 y + 26 = 0, is$

Topic: JEE PYQ

Answer: C. Full step-by-step solution below.

A $1$
B $2$
C $3$
D $4$

Correct answer: C

Solution

(c) C_{1} (2, 3) r_{1} = 5 C_{2} (- 3, - 9) r_{2} = 8 C_{1} C_{2} = 25 + 144 = 13 C_{1} C_{2} = r_{1} + r_{2} \Rightarrow externally touch \Rightarrow 3 common tangents

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